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Moving Charges And Magnetism

Magnetic field due to current element, Biot-Savart; Magnetic field on the axis of a circular current loop

  • Static charges produce an electric field while current or moving charges produce magnetic field (B).

  • Magnetic field of several sources is the vector addition of magnetic field of each individual source.

Lorentz Force

  • Consider a point charge q moving in the presence of both electric and magnetic fields.


q − Point charge

v − Velocity of point charge

t − Time

r − Distance

B (r) − Magnetic field

E (r) − Electric field

Force on the charge, = Felectric + Fmagnetic

This force is called Lorentz force.

  • Force due to magnetic field depends on q, v, B. Force on negative charge is opposite to that of positive charge.

  • Magnetic force is a vector product of velocity (v) and magnetic field (B). It vanishes, if v and B are parallel or anti-parallel.

  • Magnetic force is zero, if charge is not moving.

  • Unit of magnetic field (B) is tesla (T).

Magnetic Force on a Current Carrying Conductor Placed in Magnetic Field:

A straight rod carrying current is considered.


A − Cross-sectional area of the rod

l − Length of the rod

n − Number density of mobile charge carriers

I − Current in the rod

vd − Average drift velocity of mobile charge carrier

B − External magnetic field

Force on the carriers,

F = (nAl) qvd × B

Since current density, j = nqvd

F = [(nqvd)Al] × B

F = [jAl] × B

F = I l × B


l is the vector magnitude of length of the rod

  • For a wire of arbitrary shape,

  • When a charged particle having charge q moves inside a magnetic field with velocity v, it experiences a force .

  • When is perpendicular to, the force on the charged particle acts as the centripetal force and makes it move along a circular path.

  • Let m be the mass of charged particle and r be the radius of the circular path.

           Then qv×B=mv2r

        v and B are at right angles


  • Time period of the circular motion of a charged particle is given by



  • Angular frequency,


This is often called cyclotron frequency.

Velocity Selector

  • Force in the presence of magn…

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